The structure of critical sets
Walter Bossert (University of Montreal), Susumu Cato (University of Tokyo) and Kohei Kamaga (Sophia University)
GPI Working Paper No. 4-2025
The purpose of this paper is to address some ambiguities and misunderstandings that appear in previous studies of population ethics. In particular, we examine the structure of intervals that are employed in assessing the value of adding people to an existing population. Our focus is on critical-band utilitarianism and critical-range utilitarianism, which are commonly-used population theories that employ intervals, and we show that some previously assumed equivalences are not true in general. The possible discrepancies can be attributed to the observation that critical bands need not be equal to critical sets. The critical set for a moral quasi-ordering is composed of all utility numbers such that adding someone with a utility level in this set leads to a distribution that is not comparable to the original (non-augmented) distribution. The only case in which critical bands and critical sets coincide obtains when the critical band is an open interval. In this respect, there is a stark contrast between critical-band utilitarianism and critical-range utilitarianism: the critical set that corresponds to a critical-range quasi-ordering always coincides with the interval that is used to define the requisite quasi-ordering. As a consequence, an often presumed equivalence of critical-band utilitarianism and critical-range utilitarianism is not valid unless, again, the critical band and the critical range (and, consequently, the requisite critical sets) are given by the same open interval.
Other working papers
Once More, Without Feeling – Andreas Mogensen (Global Priorities Institute, University of Oxford)
I argue for a pluralist theory of moral standing, on which both welfare subjectivity and autonomy can confer moral status. I argue that autonomy doesn’t entail welfare subjectivity, but can ground moral standing in its absence. Although I highlight the existence of plausible views on which autonomy entails phenomenal consciousness, I primarily emphasize the need for philosophical debates about the relationship between phenomenal consciousness and moral standing to engage with neglected questions about the nature…
Population ethics with thresholds – Walter Bossert (University of Montreal), Susumu Cato (University of Tokyo) and Kohei Kamaga (Sophia University)
We propose a new class of social quasi-orderings in a variable-population setting. In order to declare one utility distribution at least as good as another, the critical-level utilitarian value of the former must reach or surpass the value of the latter. For each possible absolute value of the difference between the population sizes of two distributions to be compared, we specify a non-negative threshold level and a threshold inequality. This inequality indicates whether the corresponding threshold level must be reached or surpassed in…
The case for strong longtermism – Hilary Greaves and William MacAskill (Global Priorities Institute, University of Oxford)
A striking fact about the history of civilisation is just how early we are in it. There are 5000 years of recorded history behind us, but how many years are still to come? If we merely last as long as the typical mammalian species…